Personally I really dislike copy and paste on an iphone. It is really annoying to use and always comes up when you don't want it to.
Also, I now love my blackberry much more than I ever did the iPhone. Apps I use are available (maps, yelp, foursquare, pandora), and the multitasking and the advanced features of the OS just keep surprising me. I can use my blackberry to connect to a VPN (it's built in). Coming from the iPhone, I feel like my handcuffs have just been taken off and I'm now free to use my phone the way I want to.
Android's browser uses a long tap for cut and paste, so never had this problem.
The only way to bring up that dialog accidentally is to tap on the screen, keep your finger still for more than one second and then try to start scrolling. Seems odd for anybody to try doing that.